Low temperature heat capacities and related thermal properties of TbAl2 and HoAl2

JOURNAL OF SOLID STATE CHEMISTRY 8, 3 6 4 - 3 6 7

Low Temperature Heat Capacities and Related Thermal Properties of THAI2and HoAI2* T. W. HILL, W. E. WALLACE, R. S. C R A I G , AND T. I N O U E

Department of Chemistry, Universityof Pittsburgh, Pittsburgh,Pennsylvania15213 Received March 12, 1973 Heat capacities of TbAI2 and HoA12for the range 5 to 300 K are presented. The magnetic contribution, (Cv)mag, for TbAI2is very broad, resembling that for GdA12.(C,)mag for HoAI~is generally similar but, in addition, peaks in Cp are observed at 20 and 28 K. The measured magnetic entropies for the two compounds arc only about 80 o,~of Rln (2J F 1). The possibility cannot be excluded that the ground state is doubly degenerate in these cases. The data are treated to givevalues of the Third Law Entropy (S), H - Ho= and F - Ho°.

Introduction

Experimental Methods

This study is part of a continuing series of investigations dealing with the heat capacities of rare earth intermetallics. The present study is an extension of earlier work on several of the LnAl2 compounds (1). Most of the LnAl2 compounds (Ln is a lanthanide) become ferromagnetic at low temperatures. The destruction of ferromagnetism gives, of course, a contribution to the heat capacity. Studies of the heat capacity behavior are being undertaken in part to determine the dependence of the magnetic heat capacity on temperature. In the preceding study measurements were made on LnAI2 with Ln = La, Ce, Pr, Nd and Gd. The influence of magnetic ordering was clearly evident in the results for the Pr, Nd and Gd compounds. PrAI~ and NdA12 exhibited sharp 2-type thermal anomalies. The magnetic heat capacity for GdAI2 was not 2-type but instead was spread over a wide range of temperatures. Since GdAI2 was the only compound in the series previously studied containing a heavy rare earth [4f (7-14)], it was not clear whether its peculiar behavior was unique to Gd, characteristic of heavy rare earths or perhaps of heavy lanthanides with odd numbers o f f electrons. The present work was undertaken partly to clarify this point and partly to provide thermodynamic data for additional LnA12 compounds.

Samples were prepared using the best grade metals available commercially--99.9% pure (exclusive of possible gaseous impurities) rare earths and 99.999% pure AI. The metals were fused together by induction heating in a watercooled copper boat under argon, the so-called cold boat method. Since these compounds form congruently, only a brief strain annealling procedure (1 hr at 1000°C) was deemed necessary. The samples were analyzed by X-ray diffraction and metallographic techniques to ascertain that they were single phase materials. The diffraction results confirmed them to exist in the MgCuz structure. Masses used in the calorimeter were 58.4610 g for TbA12 and 73.9370 for HoA12. The calorimetric technique has been described in an earlier publication from this laboratory (2).

Results and Discussion Experimental results 1 are largely summarized in Figs. 1 and 2. T~ obtained from magnetic measurements (3) is also indicated on the diagrams. Clearly, the excess heat capacity

1 Tables giving the raw heat capacity data have been deposited as Document No. NAPS-02134 with ASIS National Auxiliary Publication Service, c/o CCM Information Co., 909 Third Ave., New York, NY 10022. A copy may be secured by citing the document * This work was supported by a grant from the U.S. number and by remitting $5.00 for photocopies or $1.50 for microfiche. Army Research Office, Durham. Copyright © 1973 by Academic Press, Inc. 364 All rights or reproduction in any form reserved. Printed in Great Britain

HEATCAPACITIESOF TbA12 AND HoAI2

365

2O

•oI ~6o

~16 ! ¢,

-..12

// |

s

p//

~4

"CPnon-mag

I°I// LQ°Jt

20

I

I0

i

I

I

i

l

i

60

I00

14.0

180

220

260

Temperature(K)

~o

Cpnon-mag

Tc

"5

{5o 40 >.. 30

15 I0

i

g , u 20

5

-rio

30 Zo

60

1oo

14o

leo

220

a6o

Temperalure(OK)

~,5

300

FIG. 2. Heat capacities of HoAI2 and Cp(nonmag) vs temperature.

~8

~6 3 4

20

7O

associated with the destruction of ferromagnetism in TbA12 is not A-type but is instead broad, being significant at all temperatures studied. Thus results for TbA12, an even 4 f electron system, closely resemble those for GdA12, an odd 4 f electron system. This excludes the possibility that the broad magnetic thermal anomaly is an odd 4felectron effect. Results for HoA12 upon superficial examination seem rather different from those obtained for GdA12 and TbA12 but upon more careful scrutiny they seem rather similar. The Cp data for HoA12 show pronounced peaks at about 20 and 28 K which are superimposed on a broad thermal anomaly similar to that exhibited by TbA12. The prominence of the peaks in Cp versus T plot tends to obscure the fact that the magnetic entropy associated with the peaks (i.e., that part which corresponds to the excess over the broken

I0

I0

60

FIc. 4. Magnetic heat capacity of HoAI2 vs temperature.

- - ° ' - HoAIs,

~

50 40 50 T e m p e r a t u r e (OK)

I

500

FIG. 1. Heat capacities of TbAlz and Cp(nonmag) vs temperature. For details as to how Cp(nonmag) is evaluated, see text. 70

20

'50

4.0

I 50 60 70 Temperature (*K)

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90

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FIG. 3. Magnetic heat capacity of TbA12vstemperature.

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366

HILL ET AL. TABLE I

TABLE III

MAGNETIC ENTROPIES OF TbAI2 AND HoAI2

SMOOTHED HEAT CAPACITIESAND THERMODYNAMIC VALUES FOR HoAI2

R l n ( 2 J + DO/mole K) AS(exp)(J/mole K) THAI2 HoAI2

21.3 23.5

17.4 20.2

TABLE II SMOOTHED HEAT CAPACITIESAND THERMODYNAMIC VALUES FOR THAI2

Temp. (K)

Heat capacity Entropy (H - Ho °) - ( F - Ho °) (J/mole K) (J/mole K) (J/mole)

(J/mole)

5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 50.00 55.00 60.00 70.00 80.00 90.00 100.00 110.00 120.00 130.00 140.00 150.00 •60.00 •70.00 180.00 190.00 200.00 210.00 220.00 230.00 240.00 250.00 260.00 270.00 280.00 290.00 300.00

0.22 1.69 3.94 6.80 10.03 13.66 17.41 21.23 25.03 28.74 32.31 35.72 41.97 47.46 51.97 53.95 48.91 51.39 53.81 56.07 58.16 60.02 61.67 63.13 64.41 65.54 66.53 67.39 68.16 68.84 69.45 70.01 70.55 71.07 71.59 72.14

0.14 0.65 1.75 3.26 5.12 7.27 9.65 12.23 14.95 17.78 20.69 23.64 29.63 38.60 44.46 50.10 54.93 59.29 63.50 67.57 71.51 75.32 79.01 82.58 86.03 89.36 92.58 95.70 98.71 101.63 •04.45 107.19 109.84 112.41 114.92 117.35

0.40 4.50 18.35 44.97 86.93 146.15 223.79 320.40 436.07 570.53 723.21 893.35 1282.39 1932.95 2430.90 2966.55 3471.81 8973.73 4499.73 5048.94 5620.27 6211.33 6819.94 7444.09 8081.92 8731.79 9392.23 10,061.92 10,739,76 11,424.80 12,116.29 12,813.64 13,516.45 14,224.51 14,937.77 15,656.37

0.30 2.03 7.84 20.18 40.99 71.84 114.05 168.68 236.56 3•8.33 414.46 525.27 791.59 1155.29 1570.75 2043.88 2569.94 3141.15 3755.22 4410.67 5106.17 5840.44 6612.22 7420.29 8263.42 9140.46 10,050.28 10,991.78 11,963.91 12,965.68 13,996.14 15,054.38 16,135.56 17,250.87 18,387.56 19,548.94

273.15 298.15

70.71 72.03

110.66 116.91

13,738.93 15,523.01

16,486.84 19,332.26

Temp. (K)

Heat capacity Entropy Enthalpy - ( F - Ho °) (J/mole K) (J/mole K)

(J/mole)

(J/mole)

10.00 15.00 19.50 20.00 20.50 25.00 28.00 30.00 34.00 46.00 50.00 55.00 60.00 65.00 70.00 80.00 90.00 100.00 110.00 120.00 130.00 140.00 150.00 160.00 170.00 180.00 190.00 200.00 210.00 220.00 230.00 240.00 250.00 260.00 270.00 280.00 290.00 300.00

7.84 13.03 16.40 18.10 17.48 20.00 23.72 18.84 13.70 18.89 20.86 23.36 25.90 28.42 30.84 35.37 39.50 43.24 46.63 49.68 52.41 54.84 57.01 58.94 60.65 62.16 63.50 64.69 65.76 66.72 67.58 68.38 69.11 69.79 70.43 71.03 71.60 72.13

6.21 10.49 14.27 14.70 15.16 18.51 20.99 22.47 24.45 29.30 30.96 33.06 35.20 37.37 39.57 43.99 48.40 52.76 57.04 61.23 65.32 69.29 73.15 76.90 80.52 84.03 87.43 97.72 93.90 96.98 99.97 102.86 105.67 108.39 111.04 113.61 116.11 118.55

33.40 87.12 152.23 160.76 169.99 246.31 312.13 354.90 417.94 612.02 691.51 802.06 925.03 1060.89 1209.12 1540.58 1915.30 2329.38 2779.10 3260.96 3771.68 4308.20 4867.73 5447.72 6045.86 6660.07 7288.53 7929.65 8582.02 9244.50 9916.09 10,596.0 11,283.5 11,978.0 12,679.2 13,386.6 14,099.8 14,818.5

28.68 70.25 126.04 133.29 140.75 216.41 275.63 319.18 413.41 735.82 856.33 1016.36 1187.00 1368.42 1560.77 1978.55 2440.51 7946.33 3495.39 4086.83 4719.65 5392.81 6105.14 6885.49 7642.68 8465.56 9322.96 10,213.8 11,137.0 12,091.5 13,076.3 14,090.5 15,133.2 16,203.6 17,300.8 18,424.1 19,572.7 20,746.1

273.15 298.15

70.62 72.03

111.86 118.11

12,901.3 14,685.1

17,651.9 20,527.2

line in Fig. 2) is only 3 ~ of the total magnetic entropy of the system. In regard to the magnetic contribution to entropy and heat capacity it is clear that the measured heat capacity includes lattice and

HEATCAPACITIESOF TbA12 AND HoA12 electronic contribution. Consequently an estimate of these contributions must be made to extract the magnetic heat capacity from the total. This is accomplished ordinarily by using a nonmagnetic analog of the magnetic compound. LaAI2 and LuA12 would be appropriate in this respect but data are available only for LaA12 (1). Comparing results obtained for TbA12, HoA12 and LaA12 it was found that at temperatures above Tc Cp for the lanthanum compound exceeds Cp for TbA12 and HoA12, the excess amounting to 1-2% at 300 K. This indicates that results for LaA12 do not constitute a satisfactory representation of the nonmagnetic heat capacity contributions for TbAI2 and HoAla. The studies of Hungsberg and Gschneidner (4) suggested that the large heat capacity of LaAI2 originates with the electronic term. They found ~, the electronic specific heat coefficient, for LaA12 to be 11.0 mJ/K 2 mole, which is almost double the value for LuA12, 5.7. The enlarged value for LaA12 is ascribed to the enhanced density of states resulting from the proximity of the 4flevels to the Fermi energy in LaA12. With increasing atomic number thefstates decrease in energy to a point well below the Fermi limit; under these circumstances the enhancement due to f-level proximity disappears and 7 decreases. It thus appears that y for TbA12 or HoA12 should be closer to the value for LuAI2 than that for LaA12. Accordingly a better approximation of the nonmagnetic (nm) contribution to the heat capacity C,,,, is obtained from the expression ( C~),m = ( C,)L,A12 -- (a~) T,

where A7 = ~LaAI2- •LtlA12. (Cl~)n m is plotted in Figs. 1 and 2. (Cp)mag= C ~ - ( C p ) . m . This is plotted for TbA12 and HoA12 in Figs. 3 and 4. Experimental

367

magnetic entropies together with the theoreticavalue, R l n ( 2 J + 1) are listed in Table 1. Experimental values shown in Table I are 15 to 20 7o lower than the theoretical values in keeping with experience in this laboratory with other rare earth intermetallics (1, 2, 5, 6). The cause of the discrepancy is as yet not clear. It may be due to inadequacies in estimating C,,,. Alternatively, it may be a consequence of two low lying crystal field states by coincidence having nearly the same energy so that the system behaves as if the ground state is a doublet. Detailed analysis of ErNi5 (7) shows that this situation can occur. Smoothed heat capacities and the usual derived thermodynamic properties are given in Tables II and III. These data were obtained from the raw data by standard calculational procedures. Extrapolation of Cp to 0 K was accomplished with the use of unpublished data (8) for the temperature range 1.5 to 10 K. References I. C. DEENADAS, A. W. THOMPSON, R. S. CRAIG AND W. E. WALLACE,J. Phys. Chem. Solids 32, 1853 (1971). 2. W. E. WALLACE,C. DEENADAS,A. W. THOMPSON,AND R. S. CRAIG,3". Phys. Chem. Solids 32, 805 (1971). 3. W. E. WALLACE, "Rare Earth Intermetallics." Academic Press, New York (1973), p. 35. 4. R. T. HUNGSBERGAND K. A. GSCHNEIDNER, JR., J. Phys, Chem. Solids 33, 401 (1972). 5. R. S. CRAIG, S. G. SANKAR, N. MARZOUK, V. U. S. RAO, W. E. WALLACE,AND E. SEGAL,J, Phys. Chem. Solids 33, 2267 (1972). 6. N. MARZOUK, R. S. CRAIG, AND W. E. WALLACE,J. Phys. Chem. Solids 34, 15 (1973). 7. S.G. SANKAR,D. KELLER,R. S. CRAIG,W. E. WALLACE, AND V. U. S. RAO, unpublished data. 8. C. A. BECHMAN, R. S. CRAIG, AND W. E. WALLACE, unpublished data.